1
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

On differentiation if we get $f(x, y) d y-g(x, y) d x=0$ from $2 x^2-3 x y+y^2+x+2 y-8=0$, then $\frac{g(2,2)}{f(1,1)}=$

A

$11 / 7$

B

-3

C

$-1 / 3$

D

7

2
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=e^x, h(x)=(f \circ f)(x)$, then $\frac{h^{\prime}(x)}{h(x)}=$

A

$h(x)$

B

$\frac{1}{h(x)}$

C

$\log h(x)$

D

$-\log h(x)$

3
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\sin y=\sin 3 t$ and $x=\sin t$, then $\frac{d y}{d x}=$

A

$\frac{3}{\sqrt{4-x^2}}$

B

$\frac{3}{\sqrt{1-x^2}}$

C

$\frac{1}{\sqrt{4-x^2}}$

D

$\frac{-1}{\sqrt{4-x^2}}$

4
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\sqrt{\log \left(x^2+x+1\right)+\sqrt{\cosh (2 x-3)}}$, then $f^{\prime}(0)=$

A

$\frac{1}{2 \sqrt{\sqrt{\cosh (3)}}}\left(1+\frac{\sinh (3)}{\sqrt{\cosh (3)}}\right)$

B

$\frac{1}{2 \sqrt{\sqrt{\cosh (3)}}}\left(\log 3-\frac{\sinh (3)}{\sqrt{\cosh (3)}}\right)$

C

$\frac{\log 3 \sqrt{\cosh (3)}-\sinh (3)}{2(\cosh (3))^{\frac{3}{4}}}$

D

$\frac{\sqrt{\cosh (3)}-\sinh (3)}{2(\cosh (3))^{\frac{3}{4}}}$

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